Certain it hits the wheel. Can't be certain of it goes out or not.
Spirit of the game here is a GK. Not strictly correct in law (if the ball doesn't go out) but I would argue this is similar to those ropes across 4/3g pitches.
As Rusty says if the wheel is so close then it shouldn't be there, simples! and if it shouldn't be there it's an outside influence.
I had a really wierd one, which Thankfully didn't impact the game. At a step 4 ground I frequent as an assistant referee they have a horizontal bar that connects the post and the base of the mobile goals. For what reason it is there I can't tell. But the keeper r pushed the ball, it hit this part of the frame, bobble along the line and there was a ayer for a tap in. The club claimed from their camera that the original shot had gone in but I don't think there was conclusive evidence to say it was. I might be able to find the clip.
Finally, no referee wants this AR getting involved here. It's this precise getting involved when not required that could be the determining factor in this referee not being promoted. And that could happen whatever the decision, as at least one team is now going to be irked by the refereeing TEAM. As soon as the AR gets involved, game over.